Baby soap for eczema

My son has some mild eczema and his ped recommended using Johnson and Johnson moisturizing soap (he gave us recommendations of a lotion for him I'm okay with using). Right now we are using honest co soap. But he thinks that may be contributing to the dry skin. I'm not a huge fan of J&J, what's a good soap to use instead? I have the Shea Moisture lotion but it irritated his skin even more, so I'm weary about their soap, I dont wanna pay their price again to find out it doesnt work. Any recommendations?